Late this summer, I flew from Foggia in southern Italy to Klagenfurt, Austria, as a homage to my Uncle Jack who died on a bombing mission between those two points with 70 Squadron RAF in July 1944. Climbing out of Foggia, over woods of oak, yew and pine, my eye was caught by one of the most extraordinary building sites to be found on any flight path. Halfway between the highest mountains in the Gargano, Monte Nero and Monte Calvo, I circled above what promises to be one of the most striking and popular pilgrimage shrines ever.

Designed by the Genoese architect Renzo Piano, the massive new basilica of San Giovanni Rotondo is to be the centre of the global cult of Padre Pio, the legendary Capuchin friar canonised by Pope John Paul II before half a million devotees at St Peter's Rome in June. Not that there is anything particularly special about saint-making these days. Since his election in 1978, the Pope has created 283 saints - almost as many as all his predecessors since official Vatican records began 400 years ago.

Padre Pio (Francesco Forgio, 1887-1968), though, is special. The subject of at least 600 biographies, and many more souvenir statues, prayer cards and "snowstorms", he allegedly bore the stigmata, the five bleeding wounds that marked Christ's body as he hung on the cross at Calvary. Investigated twice by the Vatican for alleged fraud and sexual misconduct, and banned from saying Mass in public at one point in the 1930s, he was reinstated with honour.

Among Padre Pio's other gifts, according to his followers, were prophecy, conversion, the reading of souls, miraculous cures and bi-location. This last meant that he could appear in two places at once. Which he did, apparently, during the second world war. Allied pilots claim to have seen the face of the saintly friar appearing in the clouds, beseeching them not to bomb San Giovanni Rotondo, his home since 1916. The sight of a giant bearded monk looming up in front of the cockpit of a Wellington or Liberator might have prompted their pilots to take evasive action, and to have dropped their bombs elsewhere.

San Giovanni Rotondo has been a place of cult religious worship since the first temple of Apollo - and later Vesta and Janus - was built there 2,500 years ago. Puglia, the local region, has been home to countless hillside shrines and grottoes over the centuries. During Padre Pio's lifetime Catholic penitents came to confess their sins to the famous stigmatic. In 1947 he heard the confession of the young Polish priest, Karol Wojtyla, who would declare him a saint 55 years later, after he became Pope. Today 7.5 million pilgrims make their way to the village of San Giovanni Rotondo each year.

No moderniser, in his final years Padre Pio railed against Vatican II and took to checking that the skirts of fashionable young women were properly modest. Offenders were sent away to let down hemlines or borrow coats. What on earth would he make of the choice of Renzo Piano as architect of the great shrine that will have penitents coming in their millions along the 18 miles of winding road from Foggia?

Piano, one of the most inventive and accomplished of today's architects, is a moderniser. "Beaubourg," he says of Paris's iconoclastic Pompidou Centre, which he began designing with Richard Rogers and Peter Rice a year after Padre Pio's death, "is a double provocation: a challenge to academicism, but also a parody of the technological imagery of our time." It is, he says, "a joyful urban machine, a creature that might have come from a Jules Verne book, or an unlikely looking ship in dry dock." Parody? Joyful? Urban? Hardly the right credentials, surely, for a penitential pilgrimage shrine dedicated to the memory and spirit of the self-flagellating Padre Pio among the thinly inhabited mountains of Puglia.

In fact, when approached in 1991 by Padre Gerardo from the monastery of San Giovanni Rotondo, Piano declined. Over the next three weeks, blessings from Padre Gerardo and the monks were faxed daily to his studio in Genoa. Piano gave in. He had, after all, designed not only one of the most popular shrines to alternative modern religion, the Pompidou Centre, but also the superb stadium at Bari, also in Puglia, a celebration of Italy's principal religion, football. Piano knows how to make big buildings beautiful. He knows how to deal with crowds, how to ennoble rather than demean mass movements of people. His design for Kansai International Airport on an artificial island in the Bay of Osaka is proof of this.

Work on the great church began in 1995. Completion is in sight, yet its construction was never meant to be hurried. This was not just a question of funding, but the fact that the new basilica was to be built of local stone. Would this impose limits on the architect's imagination? No. Piano has thought long and hard about how to reinvigorate the tradition of building in stone. He is succeeding at San Giovanni Rotondo in quietly spectacular fashion. The main span of the low-lying church's shallow central dome, designed to enfold congregations of 6,000 under its great sloping roof, is, at over 50 metres, possibly the longest supporting arch ever built out of stone.

"This is not an attempt to get into the record books," says Piano. "It is simply a desire to find out what can be done with stone today, almost 1,000 years after the Gothic cathedrals were built. Technical virtuosity is not an end itself, but meets the needs of a precise formal choice. The church at San Giovanni Rotondo springs out of the stone of the mountainside. Walls, supporting arches, and the roof will all be made of stone. We have deliberately insisted on a single material as the expressive key to the design."

Despite the daring of its construction and its immense size, the church, seen from the ground, is remarkably discreet. "In fact," says Piano, "it will not be visible until visitors are very close." A simple glass front stands in for the monumental facades we expect of major churches. This demure entrance faces a gently sloping courtyard capable of holding up to enthusiastic people.

The first thing visitors will see is a large stone wall running alongside the road leading up to the church. This will support 12 huge bells to summon the faithful to Mass, Angelus and Benediction. "The sound of the bells", says Piano, "and the great size of the wall - 25 metres at its highest point - will make it a clear landmark from a great distance."

Inside, stone floors and walls curve up, supported by stone arches arranged in a radial pattern, to create one of the most unexpected domed spaces of all times: powerful, filled with light and, in architectural terms, all but miraculous. An invention extending Piano's canon of airport terminals, art galleries and office towers, the Padre Pio church will draw people from every (or no) creed, for whom inspiring architecture is its own spiritual reward.

In architectural and spatial terms, the new church is a very long way away from Padre Pio's cell in the nearby Convent of the Capuchin Friars. Facing a chapel dedicated to the Virgin Mary, this is furnished with no more than a bed, a crucifix, a chest for linen, a bedside table, a writing table, two chairs and a small bookshelf. The public is not admitted.

Outside and beyond, San Giovanni Rotondo has become an astonishing aggregation of religious building, good, bad, indifferent, even pure kitsch. It is little short of miraculous that the Church has commissioned Renzo Piano to design and build such a powerful and populist monument. Whatever you make of the cult of the canonised Padre Pio - his bearded face beams over Renzo Piano's desk - Foggia will be a place to return to whatever your mission, wherever you choose or are ordered to fly.